Two fuzziness indexes proposed by Kaufmann: observations about them

Abstract

Professor Arnold Kaufmann did propose at least two types of indexes for estimating fuzziness in finite standard fuzzy sets. First one has an analogue formulation to that stated by Claude Shannon for measuring uncertainty in a given system. Shannon formulation estimates one type of uncertainty classified as conflict. The present paper will reveal the inconvenience of such an index for measuring fuzziness phenomena. In addition, it is proved algebraic equivalence between another index posed by Kaufmann and a fuzziness index proposed by Ronald Yager.